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An Optimally Fast Objective-Function-Free Minimization Algorithm Using Random Subspaces
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DOI：10.1007/s10957-026-03004-3.png)
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Abstract
En 中文
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this random approximation technique does not affect the convergence of the method or its evaluation complexity for the search of an epsilon-approximate first-order critical point, which is O(epsilon(-(P+1)/P)), where P is the order of derivatives used. A variant of the algorithm using approximate Hessian matrices is also analysed and shown to require at most O(epsilon(-2)) evaluations. Preliminary numerical tests show that the random-subspace technique can significantly improve performance when used with P = 2 in the correct context.
Keywords:
Nonlinear optimization
Stochastic adaptive regularisation methods
Sketching
Evaluation complexity
Objective-function-free optimization (OFFO)
Journal
J
IF:
1.5
Papers:
184
Citations:
8.2K
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Cited Papers
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